Carsten Wiuf (University of Copenhagen)
Systems of Ordinary Differential Equations (ODEs) are standard models of complex biological systems. Typically, these systems are high dimensional, have many unknown parameters and cannot be solved explicitly except in trivial cases.
In this talk I will discuss mathematical methods to analyze a system of ODEs with respect to properties of biological relevance - such as persistence (non-extinction), switching behavior and multistationarity - without having to fix parameters or perform numerical analysis. The methods draw on many areas of mathematics, such as graph theory, dynamical systems theory and algebraic geometry.
Biological applications often require surveying different mathematical models or proposing models with prescribed qualitative features that might be built experimentally. Simple analysis, ideally algorithmic, is therefore essential for usability. I will give examples of methods and applications to models of real biological systems, such as gene transcription and cell signaling. In many cases, the analysis reveals insight that might be interpreted biologically.
Michael Zock (LIF-CNRS, Marseille)
Languages are not only means of expression, but also vehicles of thought, allowing us to discover new ideas (brainstorming) or clarify existing ones by refining, expanding, illustrating more or less well specified thoughts. Of course, all this must be learned, and to this end we need resources, tools and knowledge on how to use them.
Knowledge can be encoded at various levels of abstractions, considering different units (words, sentences, texts). While semantic maps represent words and their relations at a micro-level, schematic maps (tree banks, pattern libraries) represent them combined, in larger chunks (macro-level).
We all are familiar with microscopes, maps, and navigational tools, and we normally associate them with professions having little to do with NLP. I will argue during my talk that this does not need to be so. Methaphorically speaking, we do use the very same tools to process language, regardless of the task (analysis vs. generation) and the processor (machine vs. human brain).
Dictionaries are resources, but they can also be seen as microscopes as they reveal in more detail the hidden meanings, nutshelled in a word. This kind of information display can be achieved nowadays by a simple mouse-click, even for languages whose script we cannot read (e.g. oriental languages for most Europeans). A corpus query system like Sketch Engine can reveal additionally very precious information: a word’s grammatical and collocational behaviour in texts.
Unlike inverted spyglasses, which reduce only size, macroscopes are tools that allow us to get the great picture. Even though badly needed, they are not yet available in hardware stores, but they do exist in some scientists’ minds. They are known under the headings of pattern recognition, feature detectors, etc. The resulting abstractions, models or blueprints (frames, scripts, patterns) are useful for a great number of tasks. I will illustrate this point for patterns via two examples related to real-time language production and foreign language learning (acquisition of fluency via a self-extending speakable phrasebook).
Semantic maps (wordnets, thesauri, ontologies, encyclopedias) are excellent tools for organizing words and knowledge in a huge multidimensional meaning space. Nevertheless, in order to be truly useful, i.e. to guarantee access to the stored and desired information, maps are insufficient — we also need some navigational tool(s). To illustrate this point I will present some of my ongoing work devoted to the building of a lexical compass. The assumption is that people have a highly connected conceptual-lexical network in their mind. Finding a word amounts thus to entering the network at any point by giving a related word (source word) and to follow then the links (associations) until one has reached the target word.
To allow for this kind of navigation, I believe that we need to do three things : (a) build an association network, (b) cluster the set of words, i.e. the associated terms we get in response to the input (word coming to the user's mind while trying to access the target; tip of the tongue problem), and (c) give meaningful names to the clusters. While the first step consists in building the semantic map within search takes place, the role of the next two steps is to support navigation. The role of the resulting categorial tree is to organize the set of words triggered by some input. Since any input is likely to yield many outputs (all words being associated with many other words) it is important to organize the resulting set of words, as otherwise we will drown the user.
Jaeyun Sung (Mayo Clinic, Rochester, MN, USA)
Recent advances in sequencing technologies and metagenomics have revealed statistical associations between the abundance of taxonomic groups (or their genetic repertoire) and a number of pathologies. Such descriptive, profiling investigations offer important insights into taxonomic and functional variations relevant to host health and disease; yet, a mechanistic and comprehensive understanding of those observed results remains elusive. If available, a comprehensive map of molecular interactions between microbial species could be used to integrate the vast collection of previous findings into a global network context. To this end, we present a global interspecies metabolic interaction network of the human gut microbiota. The information upon which the network architecture stands is primarily from literature-based annotations of ~570 microbial species and 3 human cell types metabolically interacting through >4,400 small-molecule transport and macromolecule degradation events. To demonstrate the utility of our network, we developed a mathematical framework for analyzing gut microbial communities in a given population, such as a cohort of type 2 diabetes (T2D) patients. In a patient population with a specific set of socio-demographic characteristics, the microbial entities abundant or scarce in T2D, and the metabolic influence connections surrounding each microbial entity, were shown in a community-scale, metabolic influence network. The influence network suggests the presence of microbial entities that impose a relatively high degree of metabolic influence to other entities. Our network presents a foundation towards integrative investigations of community-scale microbial activities within the human gut.
Alexey Snezhko (Argonne National Laboratory, USA)
Strongly interacting colloids driven out-of-equilibrium by an external periodic forcing often develop nontrivial collective dynamics. Active magnetic colloids proved to be excellent model experimental systems to explore emergent behavior and active (out-of-equilibrium) self-assembly phenomena. While colloidal systems are relatively simple, understanding their collective response, especially in out of equilibrium conditions, remains elusive.
Ferromagnetic micro-particles immersed in water and sediment on the bottom surface of the flat cell are energized by a single-axis homogeneous alternating magnetic field applied perpendicular to the surface supporting the particles. Upon application of the alternating magnetic field the magnetic torque on each particle is transferred to the mechanical torque giving rise to a rolling motion of the particle in a certain range of excitation parameters.
Experiments reveal a rich collective dynamics of magnetic rollers. Flocking and spontaneous formation of steady vortex motion have been observed. The effects are fine-tuned and controlled by the parameters of the driving magnetic field. By combing experiments and discrete particle simulations, we have identified primary physical mechanisms leading to the emergence of largescale collective motion: spontaneous symmetry breaking of the clock/counterclockwise particle rotation, collisional alignment of particle velocities, and random particle re-orientations due to shape imperfections.
Ferromagnetic micro-particles, suspended at a liquid interface and energized by a rotational homogeneous alternating magnetic field applied along the supporting interface, spontaneously form ensembles of synchronized self-assembled spinners with well-defined characteristic length. The size and the torque of an individual self-assembled spinner are controlled by the frequency of the driving magnetic field. Experiments reveal nontrivial collective dynamics in large ensembles of synchronized magnetic spinners that can spontaneously form dynamic spinner lattices at the interface in a certain range of the excitation parameters. Unusual dynamics inside of the formed spinner lattices is observed. Transport of passive cargo particles in a gas of spinners and structure of the underlying self-induced surface flows is analyzed. Active turbulent behavior of induced flows is reported.